Abstract
The first section includes additional summary statistics. The second section reports (i) estimates from the regression for the construction of our market-regulatory portfolio risk differences measure, (ii) estimates from our baseline regressions with different assumptions about standard error-clustering, (iii) results from specifications with alternative portfolio risk differences measures, (iv) weighted regressions, (v) estimates from the Heckman regressions, and (vi) results from MLE estimations.
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Table A1. Number of loans and mean and standard deviation of Portfolio risk differences by lender’s country The table reports the number of observations (loan facilities), and the mean and standard deviation of Portfolio risk differences by lender’s country.
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Table A2. OLS of Bank asset volatility on RBC ratio and RWA ratio
The table reports coefficients and t-statistics (in brackets) from the regression of Bank asset volatility on RBC ratio and on RWA ratio at the bank-year level. In specifications (1) and (2), Bank asset volatility is regressed on RBC ratio. In specifications (3) and (4), Bank asset volatility is regressed on RWA ratio. In specifications (1) and (3), the estimation method is OLS with constant. In specifications (2) and (4), the estimation method is OLS without constant. The *, **, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively.
(1) (2) (3) (4)
RBC ratio 0.027*** 0.032***
-5.897 -18.336
RWA ratio 5.293*** 5.519***
[12.955] [42.749]
Constant 0.083 0.147
-1.185 [0.584]
Observations 2,221 2,221 2,221 2,221
Adj. R-squared 0.015 0.131 0.094 0.532
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Table A3. Different loan controls
The table reports coefficients and t-statistics (in brackets). The dependent variable is AISD and all variables are defined in Table 1. The estimation method is OLS with standard errors clustered by lender’s country and bank. Each specification includes a different set of fixed effects, as given in the penultimate part of the table. The lower part of the table denotes the number of unique lenders (Number of banks) and borrowers (Number of firms) entering each specification. Different specifications include different loan controls to show that the estimates on the variable Portfolio risk differences are not overly sensitive to the loan controls used.
In specifications (1)-(3), Portfolio risk differences refers to the RBC-based Portfolio risk differences. In specifications (4)-(6), Portfolio risk differences refers to the RWA-based Portfolio risk differences. The *, **, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively.
(1) (2) (3) (4) (5) (6)
Portfolio risk differences -52.372*** -54.014** -50.232* -42.756** -44.740* -40.587*
[-2.754] [-2.229] [-2.005] [-1.971] [-1.809] [-1.794]
Constant 422.606*** 308.182*** 301.522*** 349.777*** 227.012*** 218.883***
[17.848] [15.387] [16.275] [11.858] [12.150] [11.886]
Observations 42,857 42,857 42,857 42,857 42,857 42,857
Adj. R-squared 0.787 0.781 0.781 0.787 0.781 0.781
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Table A4. Seemingly unrelated regressions
The table reports coefficients and t-statistics [in brackets]. The dependent variable is AISD and all variables are defined in Table 1. The estimation method is FGLS. The lower part of the table denotes the number of unique lenders (Number of banks) and borrowers (Number of firms) entering each specification. Different specifications include a system of regression equations to control for the simultaneous determination of loan terms in each loan facility (only the estimates from the regression where the dependent variable is AISD are reported). In each regression, the set of regressors is the same as in the regression for AISD (including AISD and excluding the variable that acts as regressand in the respective equation). In specification (1), three regression equations are estimated, where the dependent variable is AISD, Bank asset volatility, and RBC ratio respectively. In specification (2), five regression equations are estimated, where the dependent variable is AISD, Loan amount, Maturity, Collateral, and Number of lenders respectively. In specification (3), seven regression equations are estimated, where the dependent variable is AISD, Loan amount, Maturity, Collateral, Number of lenders, Bank asset volatility, and RBC ratio respectively. In specifications (1)-(3), Portfolio risk differences refers to the RBC-based Portfolio risk differences. In specifications (4)-(6), we replicate the estimations in specifications (1)-(3) by replacing the RBC-based Portfolio risk differences with the RWA-based Portfolio risk differences and RBC ratio with RWA ratio in all regression equations. The *, **, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively.
(1) (2) (3) (4) (5) (6)
Portfolio risk differences -147.188*** -115.273*** -140.589*** -303.451*** -213.395*** -316.337***
[-23.577] [-18.310] [-22.525] [-53.040] [-37.055] [-55.295]
Loan amount -12.173*** -18.767*** -19.722*** -10.516*** -16.619*** -17.187***
[-22.149] [-34.324] [-36.075] [-19.045] [-30.230] [-31.262]
Maturity 0.226*** 0.006 0.071*** 0.181*** -0.069*** 0.001
[9.791] [0.268] [3.079] [7.739] [-2.975] [0.033]
Collateral 98.764*** 172.860*** 173.184*** 94.205*** 170.414*** 167.465***
[60.776] [110.534] [110.741] [56.982] [106.808] [104.965]
Number of lenders -4.633*** -6.248*** -6.487*** -4.535*** -5.895*** -6.131***
[-18.668] [-25.281] [-26.252] [-18.028] [-23.528] [-24.472]
Performance provisions -55.213*** -47.752*** -47.388*** -54.032*** -48.465*** -47.316***
[-21.549] [-18.639] [-18.497] [-20.917] [-18.763] [-18.318]
Number of covenants -5.329*** -14.246*** -14.233*** -4.433*** -13.870*** -13.296***
[-6.392] [-17.118] [-17.102] [-5.269] [-16.513] [-15.830]
Number of participants 1.680*** 4.316*** 4.834*** 1.003*** 3.471*** 3.791***
[6.001] [15.461] [17.319] [3.554] [12.339] [13.475]
Bank asset volatility 24.672*** 16.395*** 24.807*** 44.796*** 23.778*** 45.072***
[43.612] [28.642] [43.853] [86.989] [45.198] [87.524]
Constant 178.781*** 366.622*** 280.541*** 348.768*** 463.679*** 430.875***
[15.131] [31.113] [23.820] [28.878] [38.480] [35.775]
Observations 42,857 42,857 42,857 42,857 42,857 42,857
R-squared 0.218 0.187 0.170 0.188 0.177 0.147
Number of banks 364 364 364 364 364 364
Number of firms 10,230 10,230 10,230 10,230 10,230 10,230
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Table A5. Different clustering of standard errors
The table reports coefficients and t-statistics (in brackets). The dependent variable is AISD and all variables are defined in Table 1. The estimation method is OLS. The penultimate part of the table denotes the type of fixed effects used in each specification and the type of standard error clustering (LC&Y refers to Lender’s country and Year, B&Y refers to Bank and Year, LC&B&Y refers to Lender’s country and Bank and Year). The lower part of the table denotes the number of unique lenders (Number of banks) and borrowers (Number of firms) entering each specification. In specifications (1)-(3), Portfolio risk differences refers to the RBC-based Portfolio risk differences. In specifications (4)-(6), we replicate the estimations in specifications (1)-(3) by replacing the RBC-based Portfolio risk differences with the RWA-based Portfolio risk differences. The *, **, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively.
(1) (2) (3) (4) (5) (6)
Portfolio risk differences -58.074** -58.074* -58.074** -45.406* -45.406* -45.406*
[-2.841] [-2.122] [-2.841] [-1.893] [-1.893] [-1.893]
Performance provisions -20.742*** -20.742*** -20.742*** -20.820*** -20.820*** -20.820***
[-4.856] [-4.548] [-4.856] [-5.284] [-4.604] [-5.284]
Constant 432.111*** 432.111*** 432.111*** 345.316*** 345.316*** 345.316***
[72.704] [24.105] [72.704] [12.696] [8.701] [12.696]
Observations 42,857 42,857 42,857 42,857 42,857 42,857
Adj. R-squared 0.788 0.788 0.788 0.788 0.788 0.788
Clustering LC&Y B&Y LC&B&Y LC&Y B&Y LC&B&Y
Number of banks 364 364 364 364 364 364
Number of firms 10,230 10,230 10,230 10,230 10,230 10,230
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Table A6. Different Portfolio risk differences measures
The table reports coefficients and t-statistics (in brackets). The dependent variable is AISD and all variables are defined in Table 1.
The estimation method is OLS with standard errors clustered by lender’s country and bank. Each specification includes a different set of fixed effects, as given in the penultimate part of the table. The lower part of the table denotes the number of unique lenders (Number of banks) and borrowers (Number of firms) entering each specification. Each specification includes a variation of Portfolio risk differences. Portfolio risk differences (EMU-adjusted) is the measure calculated when a common risk-free rate for all countries of the Economic and Monetary Union (EMU) is employed in Equation (4). Portfolio risk differences (OLS w/o constant) is the measure calculated when the OLS in Equation (2) is estimated without a constant. Portfolio risk differences (OLS by bank) is the measure calculated when the OLS in Equation (2) is estimated for each lender separately. In specifications (1)-(3), Portfolio risk differences refers to the RBC-based Portfolio risk differences. In specifications (4)-(6), we replicate the estimations in specifications (1)-(3) by replacing the RBC-based Portfolio risk differences with the RWA-based Portfolio risk differences. The *, **, and ***
denote statistical significance at the 10%, 5%, and 1% level, respectively.
(1) (2) (3) (4) (5) (6)
Portfolio risk differences (EMU-adjusted) -58.072*** -47.624*
[-2.741] [-1.926]
Portfolio risk differences (w/o constant) -46.157*** -37.859**
[-2.742] [-2.027]
Portfolio risk differences (OLS by bank) -42.357*** -42.563***
[-2.879] [-2.803]
Performance provisions -20.742*** -20.742*** -20.746*** -20.820*** -20.820*** -20.825***
[-6.704] [-6.704] [-6.712] [-6.673] [-6.673] [-6.701]
Constant 432.128*** 432.104*** 434.313*** 344.606*** 344.593*** 350.344***
[18.369] [18.368] [18.629] [11.867] [11.867] [11.057]
Observations 42,857 42,857 42,857 42,857 42,857 42,857
Adj. R-squared 0.788 0.788 0.788 0.788 0.788 0.788
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Table A7. Weighted regressions
The table reports coefficients and t-statistics (in brackets). The dependent variable is AISD and all variables are defined in Table 1. The estimation method is OLS with standard errors clustered by lender’s country and bank. Each specification includes a different set of fixed effects, as given in the penultimate part of the table. The lower part of the table denotes the number of unique lenders (Number of banks) and borrowers (Number of firms) entering each specification. In specification (1), we weight by the number of loans between the lender’s country and the borrower’s country to the total number of loans in our sample. In specification (2), we weight by the number of loans between the lender and the borrower’s country to the total number of loans in our sample. In specification (3), we weight by the number of loans between the lender and the borrower to the total number of loans in our sample. In specifications (1)-(3), Portfolio risk differences refers to the RBC-based Portfolio risk differences. In specifications (4)-(6), we replicate the estimations in specifications (1)-(3) by replacing the RBC-based Portfolio risk differences with the RWA-based Portfolio risk differences. The *, **, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively.
(1) (2) (3) (4) (5) (6)
Portfolio risk differences -58.358*** -58.247*** -58.168*** -45.800* -45.371** -45.457**
[-2.782] [-2.780] [-2.711] [-1.862] [-1.936] [-1.899]
Performance provisions -20.723*** -20.707*** -20.746*** -20.801*** -20.786*** -20.824***
[-6.728] [-6.745] [-6.709] [-6.693] [-6.708] [-6.673]
Constant 436.808*** 436.919*** 430.703*** 350.064*** 350.049*** 343.760***
[19.389] [17.303] [18.693] [13.332] [12.653] [11.942]
Observations 42,857 42,857 42,857 42,857 42,857 42,857
Adj. R-squared 0.788 0.788 0.788 0.788 0.788 0.788
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Table A8. Heckman sample-selection model
The table reports coefficients and t-statistics (in brackets) from Heckman’s (1979) sample-selection model. The dependent variable is in the second line of each panel and all variables are defined in Table 1. The estimation method in Panel A is maximum likelihood and in Panel B it is OLS with standard errors clustered by lender’s country and bank. Specifications (1) and (2) of Panel A report the estimates from the first-stage probit model for the determinants of the firm’s loan-taking decision. The lower part of Panel A denotes the dummy variables used in each specification. Panel B reports the estimates of the second-stage OLS regression for the effect of Portfolio risk differences on loan spreads. Each of the specifications in Panel B includes the inverse Mills ratio (Lambda) from the corresponding specification in Panel A. The penultimate part of Panel B denotes the type of fixed effects used in each specification. The lower part of Panel B denotes the number of unique lenders (Number of banks) and borrowers (Number of firms) entering each specification. In specifications (1) and (2) of Panel B, Portfolio risk differences refers to the RBC-based Portfolio risk differences. In specifications (3) and (4) of Panel B, we replicate the estimations in specifications (1) and (2) by replacing the RBC-based Portfolio risk differences with the RWA-based Portfolio risk differences. The *, **, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively.
Performance provisions -0.018 -0.018 -0.004 -0.008
[-1.548] [-1.543] [-0.332] [-0.690]
Number of covenants -0.018*** -0.016*** -0.021*** -0.022***
[-4.369] [-3.864] [-5.427] [-5.628]
Number of participants 0.089*** 0.090*** 0.090*** 0.088***
[75.346] [75.300] [75.881] [74.012]
Observations 179,590 175,947 184,612 180,891
Loan type dummies Y Y Y Y
Loan purpose dummies Y Y Y Y
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Year dummies Y Y Y Y
Firm dummies Y Y Y Y
Borrower’s country dummies Y Y Y Y
Panel B: The effect of Portfolio risk differences on loan spreads
(1)
Portfolio risk differences -46.605** -62.553*** -64.811** -53.547**
[-2.161] [-3.258] [-2.540] [-2.503]
Loan amount 301.767*** 307.592*** 270.388*** 309.525***
[11.298] [11.941] [9.876] [11.405]
Maturity -1.097*** -0.593*** -0.667*** -0.564***
[-5.716] [-3.457] [-3.282] [-3.251]
Collateral -314.537*** -263.549*** -258.198*** -274.842***
[-10.547] [-10.906] [-9.266] [-10.451]
Number of lenders 164.928*** 162.113*** 151.391*** 165.787***
[11.573] [12.268] [10.324] [11.726]
Performance provisions 13.539*** 12.753*** -12.477*** -3.824
[3.248] [3.177] [-4.306] [-1.242]
Number of covenants 33.975*** 29.540*** 37.704*** 42.590***
[8.797] [8.773] [7.663] [9.413]
Number of participants -180.629*** -178.173*** -164.392*** -180.507***
[-11.554] [-12.271] [-10.344] [-11.724]
Bank asset volatility -0.709 104.065*** 1.354 97.770***
[-0.192] [9.921] [0.385] [9.291]
Lambda -2,500.030*** -2,453.699*** -2,247.789*** -2,519.777***
[-11.558] [-12.238] [-10.004] [-11.649]
Constant -2,914.067*** -3,254.251*** -2,293.312*** -3,068.568***
[-9.952] [-10.696] [-8.540] [-10.141]
Observations 42,508 42,508 42,508 42,508
Adj. R-squared 0.830 0.835 0.817 0.828
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Table A9. Probability for break in relationship lending (MLE estimations)
The table reports coefficients and t-statistics (in brackets). The dependent variable is Break in relationship lending and all variables are defined in Table 1. The estimation method is MLE with robust standard errors. Each specification includes a different set of fixed effects, as given in the penultimate part of the table. The lower part of the table denotes the number of unique lenders (Number of banks) and borrowers (Number of firms) entering each specification. In specification (1), we include the main term of the RBC-based Portfolio risk differences. In specification (2), the RBC-based Portfolio risk differences is interacted with maturity, i.e., the loan duration (in months). In specification (3), the RBC-based Portfolio risk differences is interacted with Upfront fee, i.e., the one-time fee paid by the borrower to lender(s) at the loan closing date as a percentage of the loan facility amount. In specification (4), the RBC-based Portfolio risk differences is interacted with Firm ROA 75th, i.e., a binary variable equal to one if the firm’s return on assets (Firm ROA) is in the top 25th percentile of our sample, and zero otherwise. In specification (5), the RBC-based Portfolio risk differences is interacted with Firm Tobin’s Q 75th, i.e., if the firm’s Tobin’s Q (Firm Tobin’s Q) is in the top 25th percentile of our sample, and zero otherwise. In specifications (6)-(10), we replicate the estimations in specifications (1)-(5) by replacing the RBC-based Portfolio risk differences with the RWA-based Portfolio risk differences. The *, **, and *** denote statistical significance at the 10%, 5%, and 1% level, respectively.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Portfolio risk differences 0.244*** 0.253*** 0.177* 0.229*** 0.261*** 0.241*** 0.267*** 0.269** 0.243*** 0.271***
[4.879] [5.083] [1.659] [4.164] [4.757] [4.258] [4.710] [2.346] [3.956] [4.366]
Portfolio risk differences × Maturity
-0.006*** -0.006***
[-4.644] [-4.852]
Portfolio risk differences × 0.016* 0.016*
Upfront fee [1.673] [1.879]
Portfolio risk differences × 0.090* 0.092*
Firm ROA 75th [1.681] [1.756]
Portfolio risk differences × 0.110** 0.126*
Firm Tobin’s Q 75th [1.916] [1.873]
Observations 42,857 42,857 9,174 42,791 42,855 42,857 42,857 9,174 42,791 42,855
Adj. R-squared 0.0246 0.0264 0.0171 0.0257 0.0260 0.0244 0.0264 0.0178 0.0256 0.0259
Number of banks 364 364 233 362 364 364 364 233 362 364
Number of firms 10,230 10,230 3,286 10,230 10,230 10,230 10,230 3,286 10,230 10,230